I didn't really hear a squeak in your videos. Will just beat me to it... hubs or brakes. get you a set of jack stands and a floor jack. put the rear up in the air and put it in drive NOT in 4x4. and listen.
did you check the u-joint at the trans? since the one at the rear diff was fubar, how about the other one? or did you just replace both?
the squeak will not be in the diff at least for the parts that are lubed with the diff oil. only other place would be in the brakes/hubs.
for the rear.. drum brakes... brake dust is the #1 cause of squeaks along with out of round drums. this is something that is normal and shouldn't be anything to worry about unless you feel pulsation in the brake pedal along with the rig not stopping smoothly. if it stops smooth and there is no pulsations, and the shoes are not worn down thin. there isn't much you can do there, maybe wash out the brakes removing the dust.
the only other thing in the brakes that might make that noise would be the backing plate slightly touching the drum, there will be rub marks on the lip when you pull the drum that would be noticeable. you can also hear that if you lift the wheels off the ground and turn the tire by hand.
again the above mentioned will not be a show stopper need to fix asap thing. the things that will be a show stopper is u-joints or the diff running dry of lube.